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In this paper, we study the problem of image recognition with non-differentiable constraints. A lot of real-life recognition applications require a rich output structure with deterministic constraints that are discrete or modeled by a non-differentiable function. A prime example is recognizing digit sequences, which are restricted by such rules (e.g., \textit{container code detection}, \textit{social insurance number recognition}, etc.). We investigate the usefulness of adding non-differentiable constraints in learning for the task of digit sequence recognition. Toward this goal, we synthesize six different datasets from MNIST and Cropped SVHN, with three discrete rules inspired by real-life protocols. To deal with the non-differentiability of these rules, we propose a reinforcement learning approach based on the policy gradient method. We find that incorporating this rule-based reinforcement can effectively increase the accuracy for all datasets and provide a good inductive bias which improves the model even with limited data. On one of the datasets, MNIST\_Rule2, models trained with rule-based reinforcement increase the accuracy by 4.7\% for 2000 samples and 23.6\% for 500 samples. We further test our model against synthesized adversarial examples, e.g., blocking out digits, and observe that adding our rule-based reinforcement increases the model robustness with a relatively smaller performance drop.